Asymptotic Analysis - Volume 11, issue 3

Authors: Cordier, Stéphane | Degond, Pierre | Markowich, Peter | Schmeiser, Christian

Article Type: Research Article

Abstract: This paper is devoted to the travelling wave analysis of the Euler–Poisson model for a plasma consisting of electrons and ions. When the Debye length tends to 0, this system leads to a non-linear hyperbolic system in a non-conservative form called quasineutral Euler system. Our aim is to determine the admissible jump relations and shock solutions for the quasineutral Euler system as limits of travelling wave solutions for the Euler–Poisson system. We show that only one of the three types of travelling wave solutions converges to admissible shock solutions of the quasineutral Euler system.

DOI: 10.3233/ASY-1995-11301

Citation: Asymptotic Analysis, vol. 11, no. 3, pp. 209-240, 1995

Authors: Bourgeat, Alain | Marušić-Paloka, Eduard | Mikelić, Andro

Article Type: Research Article

Abstract: We consider the behavior of the solution to Stokes system in porous medium, with characteristic size of the pores ε and containing a thin fissure {0≤xn ≤η}, of width η. The limit when ε and η tend to zero gives the effective (or homogenized) behavior for the flow. Depending on the comparison between ε and η we obtain three possible limits: – When η<κε2/3 the fissure is not giving any contribution, i.e., the effective fluid flow is governed by the Darcy law. – When η~κε2/3 the coupling effect appears and the effective flow behaves like Darcy …flow in the porous medium coupled with the tangential flow on the surface {xn = 0}. Compared to the previous case η<ε2/3 , the effective velocity has now an additional tangential component concentrated on {xn = 0}. – When η>κε2/3 the fissure is dominant and the tangential flow at {xn = 0} is dominant. Meanwhile in the other part of the porous medium the effective velocity is equal to zero. Show more

DOI: 10.3233/ASY-1995-11302

Citation: Asymptotic Analysis, vol. 11, no. 3, pp. 241-262, 1995

Authors: van Mouche, P.

Article Type: Research Article

Abstract: Asymptotics, for coupling constant A tending to zero and to infinity, for the bands and gaps of the Schrödinger operator (HA g)(n)=g(n+1)+Abn g(n)+g(n−1) on l2 (Z) with periodic potential b are studied. In this context special attention is paid to ‘asymptotic spectral powers’. Three different perturbation techniques are used to obtain results. In this first paper the emphasis lies on results that can be obtained by a first-order degenerate or arbitrary-order non-degenerate Rayleigh–Schrödinger perturbation calculus.

DOI: 10.3233/ASY-1995-11303

Citation: Asymptotic Analysis, vol. 11, no. 3, pp. 263-287, 1995

Authors: Beretta, Elena | Vogelius, Michael

Article Type: Research Article

Abstract: We seek to identify the non-linearity of the semilinear elliptic equation, ▵u=−f(u)≤0, from boundary measurements of the normal flux corresponding to homogeneous Dirichlet data. The possibility of such identification depends crucially on the shape of the domain. In this paper we prove that identification of an analytic function f is (generically) possible if the domain has a proper corner. This result significantly extends an earlier result obtained in [2], by almost entirely eliminating the restrictions imposed on the size of the angle of the corner.

DOI: 10.3233/ASY-1995-11304

Citation: Asymptotic Analysis, vol. 11, no. 3, pp. 289-315, 1995